Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm

TL;DR

This paper introduces a hybrid genetic algorithm for the 3D Heisenberg spin glass model to analyze ground-state properties, revealing boundary condition effects on system stability.

Contribution

A novel genetic algorithm combining triadic crossover and parameter-free methods for studying Heisenberg spin glasses.

Findings

Stiffness constant $ heta=0$ with periodic-antiperiodic boundary conditions.

Stiffness constant $ heta \,\sim\, 0.62$ with open-boundary-twist conditions.

Both results indicate the ground state is stable against weak perturbations.

Abstract

We developed a genetic algorithm (GA) in the Heisenberg model that combines a triadic crossover and a parameter-free genetic algorithm. Using the algorithm, we examined the ground-state stiffness of the $\pm J$ Heisenberg model in three dimensions up to a moderate size range. Results showed the stiffness constant of $\theta = 0$ in the periodic-antiperiodic boundary condition method and that of $\theta \sim 0.62$ in the open-boundary-twist method. We considered the origin of the difference in $\theta$ between the two methods and suggested that both results show the same thing: the ground state of the open system is stable against a weak perturbation.